Basic R Commands

The commands below

  1. create vectors x and y

  2. Returning the gtheir length

  3. sum them together

  4. checking the objects present in the environment

  5. removing x and y from the environment

  6. create a 2X2 matrix with numbers from 1 to 4

  7. find the square root and the square of each matrix’s component

  8. Drawing random numbers from the Normal distribution

  9. Compute summary statistics such as sample mean, variance, standard deviation and correlation

x <- c(1,3,2,5)
x
## [1] 1 3 2 5
y = c(1,4,3)
y
## [1] 1 4 3
length(x)
## [1] 4
length(y)
## [1] 3
x+y
## Warning in x + y: longer object length is not a multiple of shorter object
## length
## [1] 2 7 5 6
ls()
## [1] "x" "y"
rm(x,y)
ls()
## character(0)
rm(list=ls())
?matrix
x=matrix(data=c(1,2,3,4), nrow=2, ncol=2)
x
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
x=matrix(c(1,2,3,4),2,2)
matrix(c(1,2,3,4),2,2,byrow=TRUE)
##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4
sqrt(x)
##          [,1]     [,2]
## [1,] 1.000000 1.732051
## [2,] 1.414214 2.000000
x^2
##      [,1] [,2]
## [1,]    1    9
## [2,]    4   16
x=rnorm(50)
y=x+rnorm(50,mean=50,sd=.1)
cor(x,y)
## [1] 0.993325
set.seed(1303)
rnorm(50)
##  [1] -1.1439763145  1.3421293656  2.1853904757  0.5363925179  0.0631929665
##  [6]  0.5022344825 -0.0004167247  0.5658198405 -0.5725226890 -1.1102250073
## [11] -0.0486871234 -0.6956562176  0.8289174803  0.2066528551 -0.2356745091
## [16] -0.5563104914 -0.3647543571  0.8623550343 -0.6307715354  0.3136021252
## [21] -0.9314953177  0.8238676185  0.5233707021  0.7069214120  0.4202043256
## [26] -0.2690521547 -1.5103172999 -0.6902124766 -0.1434719524 -1.0135274099
## [31]  1.5732737361  0.0127465055  0.8726470499  0.4220661905 -0.0188157917
## [36]  2.6157489689 -0.6931401748 -0.2663217810 -0.7206364412  1.3677342065
## [41]  0.2640073322  0.6321868074 -1.3306509858  0.0268888182  1.0406363208
## [46]  1.3120237985 -0.0300020767 -0.2500257125  0.0234144857  1.6598706557
set.seed(3)
y=rnorm(100)
mean(y)
## [1] 0.01103557
var(y)
## [1] 0.7328675
sqrt(var(y))
## [1] 0.8560768
sd(y)
## [1] 0.8560768

Activity 1

Draw 10 numbers from the normal distribution with mean 5 and variance 2. Store them in the vector x and calculate the sample mean and standard deviation. Put them in a 2 X 5 matrix by row and and raise each number to the power of three.

Graphics

The commands below show how to: 1. Do a scatter plot with the command plot and save it to a pdf file. 2. Create sequences and store them into vectors 3. Do a contour plot with the command contour. This requires three arguments: a vector of the x values, the y values and a matrix whose values correspond to each (x,y) pair (coordinates). Also do a heatmap with the command image. 4. Produce a 3-d plot for the above with the commande persp. The two arguments theta and phi control the angles at which the plot is viewed.

x=rnorm(100)
y=rnorm(100)
plot(x,y)

plot(x,y,xlab="this is the x-axis",ylab="this is the y-axis",main="Plot of X vs Y")

pdf("Figure.pdf")
plot(x,y,col="green")
dev.off()
## quartz_off_screen 
##                 2
x=seq(1,10)
x
##  [1]  1  2  3  4  5  6  7  8  9 10
x=1:10
x
##  [1]  1  2  3  4  5  6  7  8  9 10
x=seq(-pi,pi,length=50)
y=x
f=outer(x,y,function(x,y)cos(y)/(1+x^2))
contour(x,y,f)
contour(x,y,f,nlevels=45,add=T)

fa=(f-t(f))/2
contour(x,y,fa,nlevels=15)

image(x,y,fa)

persp(x,y,fa)

persp(x,y,fa,theta=30)

persp(x,y,fa,theta=30,phi=20)

persp(x,y,fa,theta=30,phi=70)

persp(x,y,fa,theta=30,phi=40)

Activity 2

Construct x and y to be sequences of length 100 from -5 to 5. Then 1. Set f1 to be 2 times x and do a scatter plot of x and f1. 2. Set f2 to be 2 times x minus 3 times y and produce a contour plot, a heatmap and 3d plot of f2 vs x and y

x=seq(-5,5,length=100)
y=x
f1=2*x
plot(x,f1)
f2=outer(x,y,function(x,y)2*x-3*y)
plot(x,f1)

contour(x,y,f2)
contour(x,y,f2,nlevels=45,add=T)

image(x,y,f2)

persp(x,y,f2)

## Indexing Data

Below are some commands for practicing in working with matrices and accessing their elements

A=matrix(1:16,4,4)
A
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16
A[2,3]
## [1] 10
A[c(1,3),c(2,4)]
##      [,1] [,2]
## [1,]    5   13
## [2,]    7   15
A[1:3,2:4]
##      [,1] [,2] [,3]
## [1,]    5    9   13
## [2,]    6   10   14
## [3,]    7   11   15
A[1:2,]
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
A[,1:2]
##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8
A[1,]
## [1]  1  5  9 13
A[-c(1,3),]
##      [,1] [,2] [,3] [,4]
## [1,]    2    6   10   14
## [2,]    4    8   12   16
A[-c(1,3),-c(1,3,4)]
## [1] 6 8
dim(A)
## [1] 4 4

Loading Data

Below are some commands for loading data from an existing file.

Auto=read.table("Auto.data.txt")
dim(Auto)
## [1] 398   9
names(Auto)
## [1] "V1" "V2" "V3" "V4" "V5" "V6" "V7" "V8" "V9"
Auto=read.table("Auto.data.txt",header=T,na.strings="?")
dim(Auto)
## [1] 397   9
names(Auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"         "origin"      
## [9] "name"
Auto=read.csv("Auto.csv",header=T,na.strings="?")
dim(Auto)
## [1] 397   9
names(Auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"         "origin"      
## [9] "name"
Auto[1:4,]
##   mpg cylinders displacement horsepower weight acceleration year origin
## 1  18         8          307        130   3504         12.0   70      1
## 2  15         8          350        165   3693         11.5   70      1
## 3  18         8          318        150   3436         11.0   70      1
## 4  16         8          304        150   3433         12.0   70      1
##                        name
## 1 chevrolet chevelle malibu
## 2         buick skylark 320
## 3        plymouth satellite
## 4             amc rebel sst
Auto=na.omit(Auto)
dim(Auto)
## [1] 392   9
names(Auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"         "origin"      
## [9] "name"

Additional Graphical and Numerical Summaries

Below are some commands to do exploratory analysis on the Auto dataset

Auto=read.csv("Auto.csv",header=T,na.strings="?")
plot(Auto$cylinders, Auto$mpg)

attach(Auto)
plot(cylinders, mpg)

cylinders=as.factor(cylinders)
plot(cylinders, mpg)

plot(cylinders, mpg, col="red")

plot(cylinders, mpg, col="red", varwidth=T)

plot(cylinders, mpg, col="red", varwidth=T,horizontal=T)

plot(cylinders, mpg, col="red", varwidth=T, xlab="cylinders", ylab="MPG")

hist(mpg)

hist(mpg,col=2)

hist(mpg,col=2,breaks=15)

pairs(Auto)

pairs(~ mpg + displacement + horsepower + weight + acceleration, Auto)

plot(horsepower,mpg)
identify(horsepower,mpg,name)

## integer(0)
summary(Auto)
##       mpg          cylinders      displacement     horsepower   
##  Min.   : 9.00   Min.   :3.000   Min.   : 68.0   Min.   : 46.0  
##  1st Qu.:17.50   1st Qu.:4.000   1st Qu.:104.0   1st Qu.: 75.0  
##  Median :23.00   Median :4.000   Median :146.0   Median : 93.5  
##  Mean   :23.52   Mean   :5.458   Mean   :193.5   Mean   :104.5  
##  3rd Qu.:29.00   3rd Qu.:8.000   3rd Qu.:262.0   3rd Qu.:126.0  
##  Max.   :46.60   Max.   :8.000   Max.   :455.0   Max.   :230.0  
##                                                  NA's   :5      
##      weight      acceleration        year           origin     
##  Min.   :1613   Min.   : 8.00   Min.   :70.00   Min.   :1.000  
##  1st Qu.:2223   1st Qu.:13.80   1st Qu.:73.00   1st Qu.:1.000  
##  Median :2800   Median :15.50   Median :76.00   Median :1.000  
##  Mean   :2970   Mean   :15.56   Mean   :75.99   Mean   :1.574  
##  3rd Qu.:3609   3rd Qu.:17.10   3rd Qu.:79.00   3rd Qu.:2.000  
##  Max.   :5140   Max.   :24.80   Max.   :82.00   Max.   :3.000  
##                                                                
##              name    
##  ford pinto    :  6  
##  amc matador   :  5  
##  ford maverick :  5  
##  toyota corolla:  5  
##  amc gremlin   :  4  
##  amc hornet    :  4  
##  (Other)       :368
summary(mpg)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    9.00   17.50   23.00   23.52   29.00   46.60

Activity 3

This exercise involves the Boston housing data set which is part of the MASS library in R. You can read about it typing ?Boston after loading the library. To load and view part of it use the following commands:

library(MASS)
head(Boston)
##      crim zn indus chas   nox    rm  age    dis rad tax ptratio  black
## 1 0.00632 18  2.31    0 0.538 6.575 65.2 4.0900   1 296    15.3 396.90
## 2 0.02731  0  7.07    0 0.469 6.421 78.9 4.9671   2 242    17.8 396.90
## 3 0.02729  0  7.07    0 0.469 7.185 61.1 4.9671   2 242    17.8 392.83
## 4 0.03237  0  2.18    0 0.458 6.998 45.8 6.0622   3 222    18.7 394.63
## 5 0.06905  0  2.18    0 0.458 7.147 54.2 6.0622   3 222    18.7 396.90
## 6 0.02985  0  2.18    0 0.458 6.430 58.7 6.0622   3 222    18.7 394.12
##   lstat medv
## 1  4.98 24.0
## 2  9.14 21.6
## 3  4.03 34.7
## 4  2.94 33.4
## 5  5.33 36.2
## 6  5.21 28.7

  1. How many rows are in this data set? How many columns? What do the rows and columns represent?

  2. Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.

  3. Are any of the predictors associated with per capita crime rate? If so, explain the relationship.

  4. Do any of the suburbs of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor.

  5. How many of the suburbs in this data set bound the Charles river?

  6. What is the median pupil-teacher ratio among the towns in this data set?

  7. Which suburb of Boston has lowest median value of owner- occupied homes? What are the values of the other predictors for that suburb, and how do those values compare to the overall ranges for those predictors? Comment on your findings.

  8. In this data set, how many of the suburbs average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the suburbs that average more than eight rooms per dwelling.

#(a)
library(MASS)
?Boston
dim(Boston)
## [1] 506  14
# 506 rows, 14 columns
# 14 features, 506 housing values in Boston suburbs

# (b)
pairs(Boston)

# X correlates with: a, b, c
# crim: age, dis, rad, tax, ptratio
# zn: indus, nox, age, lstat
# indus: age, dis
# nox: age, dis
# dis: lstat
# lstat: medv

# (c)
plot(Boston$age, Boston$crim)

# Older homes, more crime
plot(Boston$dis, Boston$crim)

# Closer to work-area, more crime
plot(Boston$rad, Boston$crim)

# Higher index of accessibility to radial highways, more crime
plot(Boston$tax, Boston$crim)

# Higher tax rate, more crime
plot(Boston$ptratio, Boston$crim)

# Higher pupil:teacher ratio, more crime

# (d)
par(mfrow=c(1,3))
hist(Boston$crim[Boston$crim>1], breaks=25)
# most cities have low crime rates, but there is a long tail: 18 suburbs appear
# to have a crime rate > 20, reaching to above 80
hist(Boston$tax, breaks=25)
# there is a large divide between suburbs with low tax rates and a peak at 660-680
hist(Boston$ptratio, breaks=25)

# a skew towards high ratios, but no particularly high ratios

# (e)
dim(subset(Boston, chas == 1))
## [1] 35 14
# (f)
median(Boston$ptratio)
## [1] 19.05
# (g)
t(subset(Boston, medv == min(Boston$medv)))
##              399      406
## crim     38.3518  67.9208
## zn        0.0000   0.0000
## indus    18.1000  18.1000
## chas      0.0000   0.0000
## nox       0.6930   0.6930
## rm        5.4530   5.6830
## age     100.0000 100.0000
## dis       1.4896   1.4254
## rad      24.0000  24.0000
## tax     666.0000 666.0000
## ptratio  20.2000  20.2000
## black   396.9000 384.9700
## lstat    30.5900  22.9800
## medv      5.0000   5.0000
#              399      406
# crim     38.3518  67.9208 above 3rd quartile
# zn        0.0000   0.0000 at min
# indus    18.1000  18.1000 at 3rd quartile
# chas      0.0000   0.0000 not bounded by river
# nox       0.6930   0.6930 above 3rd quartile
# rm        5.4530   5.6830 below 1st quartile
# age     100.0000 100.0000 at max
# dis       1.4896   1.4254 below 1st quartile
# rad      24.0000  24.0000 at max
# tax     666.0000 666.0000 at 3rd quartile
# ptratio  20.2000  20.2000 at 3rd quartile
# black   396.9000 384.9700 at max; above 1st quartile
# lstat    30.5900  22.9800 above 3rd quartile
# medv      5.0000   5.0000 at min
summary(Boston)
##       crim                zn             indus            chas        
##  Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  
##  1st Qu.: 0.08204   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  
##  Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  
##  Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  
##  3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  
##  Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  
##       nox               rm             age              dis        
##  Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  
##  1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  
##  Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  
##  Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  
##  3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  
##  Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  
##       rad              tax           ptratio          black       
##  Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   :  0.32  
##  1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.:375.38  
##  Median : 5.000   Median :330.0   Median :19.05   Median :391.44  
##  Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :356.67  
##  3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:396.23  
##  Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :396.90  
##      lstat            medv      
##  Min.   : 1.73   Min.   : 5.00  
##  1st Qu.: 6.95   1st Qu.:17.02  
##  Median :11.36   Median :21.20  
##  Mean   :12.65   Mean   :22.53  
##  3rd Qu.:16.95   3rd Qu.:25.00  
##  Max.   :37.97   Max.   :50.00
# Not the best place to live, but certainly not the worst.

# (h)
dim(subset(Boston, rm > 7))
## [1] 64 14
dim(subset(Boston, rm > 8))
## [1] 13 14
summary(subset(Boston, rm > 8))
##       crim               zn            indus             chas       
##  Min.   :0.02009   Min.   : 0.00   Min.   : 2.680   Min.   :0.0000  
##  1st Qu.:0.33147   1st Qu.: 0.00   1st Qu.: 3.970   1st Qu.:0.0000  
##  Median :0.52014   Median : 0.00   Median : 6.200   Median :0.0000  
##  Mean   :0.71879   Mean   :13.62   Mean   : 7.078   Mean   :0.1538  
##  3rd Qu.:0.57834   3rd Qu.:20.00   3rd Qu.: 6.200   3rd Qu.:0.0000  
##  Max.   :3.47428   Max.   :95.00   Max.   :19.580   Max.   :1.0000  
##       nox               rm             age             dis       
##  Min.   :0.4161   Min.   :8.034   Min.   : 8.40   Min.   :1.801  
##  1st Qu.:0.5040   1st Qu.:8.247   1st Qu.:70.40   1st Qu.:2.288  
##  Median :0.5070   Median :8.297   Median :78.30   Median :2.894  
##  Mean   :0.5392   Mean   :8.349   Mean   :71.54   Mean   :3.430  
##  3rd Qu.:0.6050   3rd Qu.:8.398   3rd Qu.:86.50   3rd Qu.:3.652  
##  Max.   :0.7180   Max.   :8.780   Max.   :93.90   Max.   :8.907  
##       rad              tax           ptratio          black      
##  Min.   : 2.000   Min.   :224.0   Min.   :13.00   Min.   :354.6  
##  1st Qu.: 5.000   1st Qu.:264.0   1st Qu.:14.70   1st Qu.:384.5  
##  Median : 7.000   Median :307.0   Median :17.40   Median :386.9  
##  Mean   : 7.462   Mean   :325.1   Mean   :16.36   Mean   :385.2  
##  3rd Qu.: 8.000   3rd Qu.:307.0   3rd Qu.:17.40   3rd Qu.:389.7  
##  Max.   :24.000   Max.   :666.0   Max.   :20.20   Max.   :396.9  
##      lstat           medv     
##  Min.   :2.47   Min.   :21.9  
##  1st Qu.:3.32   1st Qu.:41.7  
##  Median :4.14   Median :48.3  
##  Mean   :4.31   Mean   :44.2  
##  3rd Qu.:5.12   3rd Qu.:50.0  
##  Max.   :7.44   Max.   :50.0
summary(Boston)
##       crim                zn             indus            chas        
##  Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  
##  1st Qu.: 0.08204   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  
##  Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  
##  Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  
##  3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  
##  Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  
##       nox               rm             age              dis        
##  Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  
##  1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  
##  Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  
##  Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  
##  3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  
##  Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  
##       rad              tax           ptratio          black       
##  Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   :  0.32  
##  1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.:375.38  
##  Median : 5.000   Median :330.0   Median :19.05   Median :391.44  
##  Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :356.67  
##  3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:396.23  
##  Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :396.90  
##      lstat            medv      
##  Min.   : 1.73   Min.   : 5.00  
##  1st Qu.: 6.95   1st Qu.:17.02  
##  Median :11.36   Median :21.20  
##  Mean   :12.65   Mean   :22.53  
##  3rd Qu.:16.95   3rd Qu.:25.00  
##  Max.   :37.97   Max.   :50.00
# relatively lower crime (comparing range), lower lstat (comparing range)